ABC Bookstore sells new books, n, for $12, and used books, u, for $8. The store earned $112 revenue last month. The store sold 4 more used books
than new books. Which system of equations represents this scenario?
O A. 8n+ 12u= 112; u= n +4
O B. 8n + 12u=112; U= n- 4
OC. 12n+8u=112; u=n+4
O D. 12n + 8u= 112; u = n-4

D.) $12n + $8u = 112 ;u = 4 + n

Step-by-step explanation:

Given that :

Cost per new books (n) = $12

Cost per used book (u) = $8

Total revenue earned = $112

store sold 4 more used books than new books

Hence,

Total revenue should be :

Revenue from new books + Revenue from used book = total revenue

Revenue from new books = $12 * n = $12n

Revenue from used books = $8 * n = $8n

$12n + $8u = 112

Number of books sold :

Number of used books sold = 4 + number of new books sold

u = 4 + n

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!